lmomgpa: L-moments of the Generalized Pareto Distribution

In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

L-moments of the Generalized Pareto Distribution

Description

This function estimates the L-moments of the Generalized Pareto distribution given the parameters (\xi, \alpha, and \kappa) from pargpa. The L-moments in terms of the parameters are

\lambda_1 = \xi + \frac{\alpha}{\kappa+1} \mbox{,}

\lambda_2 = \frac{\alpha}{(\kappa+2)(\kappa+1)} \mbox{,}

\tau_3 = \frac{(1-\kappa)}{(\kappa+3)} \mbox{, and}

\tau_4 = \frac{(1-\kappa)(2-\kappa)}{(\kappa+4)(\kappa+3)} \mbox{.}

Usage

lmomgpa(para)

Arguments

para	The parameters of the distribution.

Value

An R list is returned.

lambdas	Vector of the L-moments. First element is \lambda_1, second element is \lambda_2, and so on.
ratios	Vector of the L-moment ratios. Second element is \tau, third element is \tau_3 and so on.
trim	Level of symmetrical trimming used in the computation, which is 0.
leftrim	Level of left-tail trimming used in the computation, which is NULL.
rightrim	Level of right-tail trimming used in the computation, which is NULL.
source	An attribute identifying the computational source of the L-moments: “lmomgpa”.

Author(s)

W.H. Asquith

References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

See Also

pargpa, cdfgpa, pdfgpa, quagpa

Examples

lmr <- lmoms(c(123,34,4,654,37,78))
lmr
lmomgpa(pargpa(lmr))

lmomco documentation built on May 29, 2024, 10:06 a.m.